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How to Bound Equations that Get Larger on the ACT

4/4/2018

 
Equations on the ACT
Photo by Antoine Dautry on Unsplash

Problem:

In the equation r = 4/(2 + k), k represents a positive integer. As k gets larger without bound, the value of r:

F. gets closer and closer to 4.
G. gets closer and closer to 2.
H. gets closer and closer to 0.
J. remains constant.
K. gets larger and larger 

Answer:

Answer is H.

As k gets larger and larger without bound, the expression 4/(2+k) becomes 4 divided by an increasingly large number. For example, think about the trend between the following fractions:

4/100,
4/10,000,
4/1,000,000, ...


Looking at it this way, you can see that the expression for r gets closer and closer to zero. 
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How to Enjoy Jane Eyre on the ACT

4/2/2018

 
jane eyre on the act
Seeing me, she roused herself: she made a sort of effort to smile, and framed a few words of congratulations; but the smile expired, and the sentence was abandoned unfinished. She put up her spectacles and pushed her chair back from the table. 

“I feel so astonished,” she began, “I hardly know what to say to you, Miss Eyre. I have surely not been dreaming, have I? Sometimes I half fall asleep when I am sitting alone and fancy things that have never happened. It has seemed to me more than once when I have been in a doze, that my dear husband, who died fifteen years since, has come in and sat down beside me; and that I have even heard him call me by my name, Alice, as he used to do. Now, can you tell me whether it is actually true that Mr. Rochester has asked you to marry him? Don’t laugh at me. But I really thought he came in here five minutes ago, and said that in a month you would be his wife.” [10]

“He has said the same thing to me,” I replied.

“He has! Do you believe him? Have you accepted him?”

“Yes.”

She looked at me bewildered.

“I could never have thought it. He is a proud man; all the Rochesters were proud: and his father at least, liked money. He, too, has always been called careful.

He means to marry you?” “He tells me so.”

She surveyed my whole person: in her eyes I read 30 that they had there found no charm powerful enough to solve the enigma.

“It passes me!” she continued; “but no doubt it is true since you say so. How it will answer I cannot tell: I really don’t know. Equality of position and fortune is often advisable in such cases; and there are twenty years of difference in your ages. He might almost be your father.” [22]

“No, indeed, Mrs. Fairfax!” I exclaimed, nettled; “he is nothing like my father! No one, who saw us 40 together, would suppose it for an instant. Mr. Rochester looks as young, and is as young, as some men at five and twenty.”

“Is it really for love he is going to marry you?” she asked.

​I was so hurt by her coldness and skepticism, that the tears rose to my eyes.

“I am sorry to grieve you,” pursued the widow; “but you are so young, and so little acquainted with men, I wished to put you on your guard. It is an old saying that ‘all is not gold that glitters’; and in this case I do fear there will be something found to be different to what either you or I expect.” [30]

“Why?—am I a monster?” I said: “Is it impossible that Mr. Rochester should have a sincere affection for me?”

“No: you are very well; and much improved of late; and Mr. Rochester, I dare say, is fond of you. I have always noticed that you were a sort of pet of his. There are times when, for your sake, I have been a little uneasy at his marked preference, and have wished to put you on your guard; but I did not like to suggest even the possibility of wrong. I knew such an idea would shock, perhaps offend you; and you were so discreet, and so thoroughly modest and sensible, I hoped you might be trusted to protect yourself. Last night I cannot tell you what I suffered when I sought all over the house, and could find you nowhere, nor the master either; and then, at twelve o’clock, saw you come in with him.

“Well never mind that now,” I interrupted impatiently; “it is enough that all was right.” [40]

“I hope all will be right in the end,” she said: “but, believe me, you cannot be too careful. Try and keep Mr. Rochester at a distance: distrust yourself as well as him. Gentlemen in his station are not accustomed to marry their governesses.” 

Questions:

1. When Mrs. Fairfax says, “Gentlemen in his station are not accustomed to marry their governesses,” she is expressing her belief that:

A. Mr. Rochester is incapable of loving Miss Eyre.
B. 
Mr. Rochester will treat Miss Eyre like a governess when they are married.
C. 
Mr. Rochester may not be sincere about his feeling towards Miss Eyre
D. 
Mr. Rochester may not really have asked Miss Eyre to marry him.

2. It can be reasonably inferred from the conversation that Mrs. Fairfax believes Miss Eyre will: 

F. recognize that Mr. Rochester actually wants to marry Mrs. Fairfax.
G. 
marry Mr. Rochester much sooner than originally planned.
H. 
no longer desire to marry Mr. Rochester.
J. potentially regret her decision to agree to marry Mr. Rochester.

3. 
Mrs. Fairfax’s opinion about Miss Eyre and Mr. Rochester’s relationship can best be exemplified by which of the following quotations from the passage? 

A. “Mr. Rochester looks as young, and is as young, as 
some men at five and twenty.” 
B. 
“How it will answer I cannot tell: I really don’t know.”
C. “He is a proud man; all the Rochesters were proud.”
D. 
“But I really thought he came in here five minutes ago, and said that in a month you would be his wife.” ​

4. The phrase “you were so discreet, and so thor- oughly modest and sensible” (lines 36–37) is used by Mrs. Fairfax to: 

F. explain why Miss Eyre should not marry Mr. Rochester.
G. 
explain why it is likely that Mr. Rochester really does not plan on marrying Miss Eyre.
H. explain why Mrs. Fairfax had not discussed Mr. Rochester’s feelings toward Miss Eyre before.
J. insult Miss Eyre and let her know that Mrs. Fairfax was disappointed in her. 


5. The passage makes it clear that Miss Eyre and Mr. Rochester:

A. get married.
B. do not really know each other well enough to become engaged.
C. will not live happily because they will be shunned by society.
D. have a relationship that is not typical in their society. 

Answers:


  1. C. The sentence before the quote states, “but, believe me, you cannot be too careful. Try and keep Mr. Rochester at a distance: distrust yourself as well as him.” Mrs. Fairfax is suggesting that Mr. Rochester’s feelings should not be trusted because they may not be genuine. This best supports answer choice C.
  2. J. Mrs. Fairfax states, “It is an old saying that ‘all is not gold that glitters’; and in this case I do fear there will be something found to be different to what either you or I expect.” This shows that Mrs. Fairfax believes Miss Eyre will discover that things may not turn out as she hoped or expected and may regret her decision. The other answer choices are not supported by the passage.
  3. B. Mrs. Fairfax says, “Gentle-men in his station are not accustomed to marry their governesses.” She is pointing out a difference in Miss Eyre and Mr. Rochester’s position and fortune and hinting that this difference is not a good thing. Mrs. Fairfax also clearly indicates that she is uncertain about Miss Eyre’s future with Mr. Rochester. This information best supports answer choice B.
  4. H. Mrs. Fairfax is explaining that she would have cautioned Miss Eyre against forming a relationship with Mr. Rochester, but Miss Eyre had seemed mature and wise enough to conclude on her own that forming an intimate relationship with Mr. Rochester would be unwise. This best supports answer choice H.
  5. D. Mrs. Fairfax states, “Gentlemen in his station are not accustomed to marry their governesses.” The words, “not accustomed to” imply that this is not a common occurrence, and that their relationship is not typical. The other answer choices are not supported by the passage. 
Ref: McGraw Hill
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How to Deal with Factored Form on the ACT

3/29/2018

 
Factoring Form ACT
Photo by Antoine Dautry on Unsplash

Question


Which of the following is a factored form of 3x^3y^3 + 3xy?

A. 3xy(x^2y^2 + 1)
B. 3(3x^2y^2)
C. (3x + 3y)(3x + 3y)
D. 3x^2y^2(xy)
E. 3x(x^2y^2 + 3) 


Answer


The correct answer is A.

This problem requires you to find the Greatest Common Factor. The Greatest Common Factor is 3xy, because each term has at least 1 factor of 3, 1 factor of x, and 1 factor of y. When you factor 3xy out of 3x^3y^3 you are left with x^2 y^2 , and when you factor 3xy out of 3xy, you are left with 1. Therefore, when factored, 3x^3 y^3 + 3xy = 3xy(x^2 y^2 + 1). 

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How to Classify the 400 Known Planets on the SAT

3/19/2018

 
Types of Planets ACT Science
Astronomers have found over 400 planets orbiting stars. The discovered planets have a variety of compositions, masses, and orbits. Despite the variety, the universal rules of physics and chemistry allow scientists to broadly categorize these planets into just a few types: Gas Giant, Carbon Orb, Water World, and Rocky Earth. Table 1 shows the composition of the various planet types and typical mass ranges relative to Earth.
ACT Science Astronomy T1
Table 2 shows a sampling of planets orbiting various stars described in Table 1. These planets are merely numbered 1-7. Table 2 details the masses and orbital radii of the planets.
ACT Science Astronomy T2

Questions:

1. The data in Table 1 and Table 2 support which of the following statements?
​
A. Gas Giant planets have the largest orbital radii.
B. Orbital radius is directly related to mass.
C. Orbital radius is inversely related to mass.
D. The data does not support a correlation between mass and orbital radius.
2. According to Table 1 and Table 2, which of the following stars has the most massive Gas Giant planet orbiting it?

F. Gliese 777
G. OGLE TR 132
H. PSR 1257
J. Gleise 581
3. If a new planet were discovered, with a mass of 325, an orbital radius of 1.5, and a composition of mostly hydrogen, what would be its most likely classification?

A. Carbon Orb
B. Water
C. Rocky Earth
D. Gas Giant

Answers

1. D
2. F
3. D
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How I Improved My 240 Common Spelling Mistakes in English In One Day

2/20/2018

 
Avoid these Spelling Errors
Image from Pixabay
​ A

·       absence
·       acceptable
·       accessible
·       accommodation
·       accomplish
·       achievement
·       acquire
·       address
·       advertisement
·       advice – (noun)
·       advise – (verb)
·       amateur
·       apartment
·       appearance
·       argument
·       athletic
·       attendance

B

·       basically
·       beginning
·       belief – indicating the noun
·       believe – indicating the verb
·       beneficial
·       business

C

·       calendar
·       campaign
·       category
·       cemetery
·       challenge
·       characteristic
·       cigarette
·       clothes
·       column
·       committee
·       commitment
·       completely
·       condemn
·       conscience
·       conscientious
·       conscious
·       controversy
·       convenient
·       correspondence
·       criticism

D

·       deceive
·       definitely
·       definition
·       department
·       describe
·       despair
·       desperate
·       development
·       difference
·       difficult
·       disappointed
·       discipline
·       disease

E

·       easily
·       effect
·       eighth
·       either
·       embarrass
·       encouragement
·       enemy
·       entirely
·       environment
·       especially
·       exaggerate
·       excellent
·       existence
·       experience
·       experiment

F

·       familiar
·       February
·       finally
·       financial
·       foreign
·       foreigner
·       formerly
·       forty
·       fourth

G

·       general
·       generally
·       genius
·       government
·       grammar
·       grateful
·       guarantee
·       guidance

H

·       happily
·       height
·       heroes
·       humorous
·       hypocrite

I

·       ideally
·       imaginary
·       immediate
·       incredible
·       independent
·       influential
·       insurance
·       intelligent
·       interference
·       interrupt
·       introduce
·       island
·       its – for possession
·       it’s – for “it is” or “it has”

J

·       jealous
·       jealousy

K

·       kneel
·       knowledge

L

·       later
·       legitimate
·       length
·       library
·       lightning
·       likely
·       loneliness
·       lose (verb)
·       loose (adjective)
·       lovely
·       luxurious

M

·       maintain
·       maintenance
·       manageable
·       management
·       manufacture
·       marriage
·       married
·       millionaire
·       misspell
·       mischievous
·       money
·       mortgage
·       muscle
·       mysterious

N

·       naturally
·       necessary
·       neighbor / neighbour
·       ninety
·       noticeable
·       nowadays

O

·       obedient
·       obstacle
·       occasional
·       occurred
·       official
·       opinion
·       opportunity
·       opposition
·       ordinary
·       originally

P

·       particular
·       peculiar
·       perceive
·       performance
·       permanent
·       personal
·       personnel
·       physical
·       physician
·       piece
·       pleasant
·       possession
·       possible
·       possibility
·       potatoes
·       practically
·       prefer
·       privilege
·       professor
·       professional
·       pronounce / pronunciation
·       psychology
·       psychological

Q

·       quantity
·       quality
·       questionnaire
·       queue
·       quizzes

R

·       realistic
·       realize
·       really
·       receipt
·       receive
·       recognize
·       recommend
·       religion
·       religious
·       remember
·       representative
·       restaurant
·       rhythm
·       ridiculous
·       roommate

 

S

·       sacrifice
·       safety
·       scared
·       scenery
·       schedule
·       secretary
·       sentence
·       separate
·       similar
·       sincerely
·       strength
·       surprise
·       suspicious
·       success
·       successful

T

·       technical
·       technique
·       temperature
·       temporary
·       their (possessed by them)
·       there (not here)
·       they’re (contraction of “they are”)
·       themselves – not themself

U

·       undoubtedly
·       unforgettable
·       unique
·       until

V

·       valuable
·       village
·       violence
·       violent
·       vision
·       volume

W

·       weather – indicating climate – The weather is nice today.
·       Wednesday
·       weird
·       whether – (indicating if)
·       which
·       woman – (singular)
·       women – (plural)
·       worthwhile
·       width
·       writing

X Y Z

·       yacht
·       young



 
 
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How to Build a Great Vocabulary 'Very' Quickly

1/26/2018

 
Build a Great Vocubulary
Photo by Amador Loureiro on Unsplash
Building a vocabulary is hard. You have to read a lot. We mean a lot. Read. Read. Read. However, when you are faced with standardized tests, like the ACT, SAT, GRE, GMAT, HSPT, ISEE, SSAT, LSAT, etc. you don't have much time to build a great vocabulary, if you already don't have one.

Here is a handy tip to quickly build a great one if you are pressed for time.

Replace the word 'very' with a new word!

  1. parched instead of "very dry"
  2. squalid instead of "very dirty"
  3. ​terrified instead of "very afraid"
  4. furious instead of "very angry"
  5. exquisite instead of "very beautiful"
  6. ​hideous instead of "very ugly"
  7. vivacious instead of "very lively"
  8. immense instead of "very big"
  9. tiny instead of "very small"
  10. spacious instead of "very roomy"
  11. precious instead of "very valuable"​
  12. mindful instead of "very aware"
  13. precise instead of "very accurate"​
  14. rudimentary instead of "very basic"​
  15. meticulous instead of "very careful"​
  16. rotten instead of "very bad"​
  17. courteous instead of "very civil"​
  18. vivid instead of "very colorful"​
  19. brilliant instead of "very clever"​
  20. meticulous instead of "very clean"​
  21. fascinating instead of "very interesting"​
  22. envious instead of "very jealous"​
  23. scorching instead of "very hot"​
  24. imminent instead of "very likely"​
  25. perilous instead of "very dangerous"
  26. filthy instead of "very dirty"
  27. arduous instead of "very difficult"
  28. tenacious instead of "very determined"
  29. fervent instead of "very eager"
  30. effortless instead of "very easy"
  31. skeptical instead of "very dubious"
  32. swift instead of "very fast"
  33. renowned instead of "very famous"
  34. ferocious instead of "very fierce"
  35. doting instead of "very fond"
  36. lithe instead of "very graceful"
  37. exasperating instead of "very frustrating"
  38. ponderous instead of "very heavy"
  39. hirsute instead of "very hairy"
  40. famished instead of "very hungry"
  41. infirm instead of "very ill"
  42. peerless instead of "very rare"
  43. conscientious instead of "very responsible"
  44. pristine instead of "very pure"
  45. depraved instead of "very immoral"
  46. humongous instead of "very large"
  47. opulent instead of "very lavish"
  48. forlorn instead of "very lonely"
  49. novel instead of "very new"
  50. precise instead of "very specific"
  51. acerbic instead of "very sour"
  52. remorseful instead of "very sorry"
  53. stern instead of "very strict"
  54. vacuous instead of "very stupid"
  55. hideous instead of "very ugly"
  56. unjust instead of "very unfair"
  57. improbable instead of "very unlikey"
  58. extraordinary instead of "very unusual"
  59. precious instead of "very valuable"
  60. abusive instead of "very violent"
  61. sage instead of "very wise"
  62. fledgling instead of "very young"
  63. untamed instead of "very wild"
  64. expansive instead of "very wide"
  65. hale instead of "very healthy"
  66. vital instead of "very important"
  67. succulent instead of "very juicy"
  68. adored instead of "very loved"
  69. blessed instead of "very lucky"
  70. furious instead of "very angry"
  71. fretful instead of "very anxious"
  72. tedious instead of "very boring"
  73. stunning instead of "very beautiful"
  74. poised instead of "very confident"
  75. frigid instead of "very cold"
  76. baffled instead of "very confused"
  77. inquisitive instead of "very curious"
  78. contorted instead of "very deformed"
  79. fragile instead of "very delicate"
  80. temperamental instead of "very emotional"
  81. melodramatic instead of "very dramatic"
  82. obese instead of "very fat"
  83. gregarious instead of "very friendly"
  84. ecstatic instead of "very happy"
  85. frank instead of "very honest"
  86. gifted instead of "very intelligent"
  87. infantile instead of "very childish"
  88. casual instead of "very informal"
  89. severe instead of "very intense"
  90. pessimistic instead of "very negative"
  91. apparent instead of "very obvious"
  92. destitute instead of "very poor"
  93. germane instead of "very relevant"
  94. boisterous instead of "very rowdy"
  95. optimistic instead of "very positive"
  96. crooked instead of "very corrupt"
  97. precarious instead of "very risky"
  98. unyielding instead of "very firm"
  99. exorbitant instead of "very expensive"
  100. ebullient instead of "very enthusiastic"
As a bonus, below is a list of the top 100 words on the SAT.

Top 100 words on the SAT

  1. abate
    become less in amount or intensity
  2. abdicate
    give up, such as power, as of monarchs and emperors
  3. aberration
    a state or condition markedly different from the norm
  4. abstain
    choose not to consume
  5. adversity
    a state of misfortune or affliction
  6. aesthetic
    characterized by an appreciation of beauty or good taste
  7. amicable
    characterized by friendship and good will
  8. anachronistic
    chronologically misplaced
  9. arid
    lacking sufficient water or rainfall
  10. asylum
    a shelter from danger or hardship
  11. benevolent
    showing or motivated by sympathy and understanding
  12. bias
    a partiality preventing objective consideration of an issue
  13. boisterous
    full of rough and exuberant animal spirits
  14. brazen
    unrestrained by convention or propriety
  15. brusque
    marked by rude or peremptory shortness
  16. camaraderie
    the quality of affording easy familiarity and sociability
  17. canny
    showing self-interest and shrewdness in dealing with others
  18. capacious
    large in the amount that can be contained
  19. capitulate
    surrender under agreed conditions
  20. clairvoyant
    someone who can perceive things not present to the senses
  21. collaborate
    work together on a common enterprise or project
  22. compassion
    a deep awareness of and sympathy for another's suffering
  23. compromise
    an accommodation in which both sides make concessions
  24. condescending
    characteristic of those who treat others with arrogance
  25. conditional
    imposing or depending on or containing an assumption
  26. conformist
    someone who follows established standards of conduct
  27. conundrum
    a difficult problem
  28. convergence
    the act of coming closer
  29. deleterious
    harmful to living things
  30. demagogue
    a leader who seeks support by appealing to popular passions
  31. digression
    a message that departs from the main subject
  32. diligent
    quietly and steadily persevering in detail or exactness
  33. discredit
    the state of being held in low esteem
  34. disdain
    lack of respect accompanied by a feeling of intense dislike
  35. divergent
    tending to move apart in different directions
  36. empathy
    understanding and entering into another's feelings
  37. emulate
    strive to equal or match, especially by imitating
  38. enervating
    causing weakness or debilitation
  39. ephemeral
    anything short-lived, as an insect that lives only for a day
  40. evanescent
    tending to vanish like vapor
  41. exemplary
    worthy of imitation
  42. extenuating
    partially excusing or justifying
  43. florid
    elaborately or excessively ornamented
  44. forbearance
    a delay in enforcing rights or claims or privileges
  45. fortitude
    strength of mind that enables one to endure adversity
  46. fortuitous
    occurring by happy chance
  47. foster
    providing nurture though not related by blood or legal ties
  48. fraught
    filled with or attended with
  49. frugal
    avoiding waste
  50. hackneyed
    repeated too often; overfamiliar through overuse
  51. haughty
    having or showing arrogant superiority
  52. hedonist
    someone motivated by desires for sensual pleasures
  53. hypothesis
    a tentative insight that is not yet verified or tested
  54. impetuous
    characterized by undue haste and lack of thought
  55. impute
    attribute or credit to
  56. inconsequential
    lacking worth or importance
  57. inevitable
    incapable of being avoided or prevented
  58. intrepid
    invulnerable to fear or intimidation
  59. intuitive
    spontaneously derived from or prompted by a natural tendency
  60. jubilation
    a feeling of extreme joy
  61. lobbyist
    someone who is employed to persuade how legislators vote
  62. longevity
    the property of having lived for a considerable time
  63. mundane
    found in the ordinary course of events
  64. nonchalant
    marked by blithe unconcern
  65. opulent
    rich and superior in quality
  66. orator
    a person who delivers a speech
  67. ostentatious
    intended to attract notice and impress others
  68. parched
    dried out by heat or excessive exposure to sunlight
  69. perfidious
    tending to betray
  70. pragmatic
    concerned with practical matters
  71. precocious
    characterized by exceptionally early development
  72. pretentious
    creating an appearance of importance or distinction
  73. procrastinate
    postpone doing what one should be doing
  74. prosaic
    lacking wit or imagination
  75. prosperity
    the condition of having good fortune
  76. provocative
    serving or tending to excite or stimulate
  77. prudent
    marked by sound judgment
  78. querulous
    habitually complaining
  79. rancorous
    showing deep-seated resentment
  80. reclusive
    withdrawn from society; seeking solitude
  81. reconciliation
    the reestablishment of cordial relations
  82. renovation
    the act of improving by renewing and restoring
  83. restrained
    under control
  84. reverence
    a feeling of profound respect for someone or something
  85. sagacity
    the ability to understand and discriminate between relations
  86. scrutinize
    examine carefully for accuracy
  87. spontaneous
    said or done without having been planned in advance
  88. spurious
    plausible but false
  89. submissive
    inclined or willing to give in to orders or wishes of others
  90. substantiate
    establish or strengthen as with new evidence or facts
  91. subtle
    difficult to detect or grasp by the mind or analyze
  92. superficial
    of, affecting, or being on or near the surface
  93. superfluous
    more than is needed, desired, or required
  94. surreptitious
    marked by quiet and caution and secrecy
  95. tactful
    having a sense of what is considerate in dealing with others
  96. tenacious
    stubbornly unyielding
  97. transient
    lasting a very short time
  98. venerable
    profoundly honored
  99. vindicate
    show to be right by providing justification or proof
  100. wary
    marked by keen caution and watchful prudence
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Want to Soar on the ACT? You Need to Know How to Tackle Pronoun Usage

11/28/2017

 
Pronouns are small (I, me, he, she, it), but they are among the biggest troublemakers in the language.

​For example, in Shakespeare's Hamlet, Ophelia cried "Woe is me," which in today's formalized English should be "Woe is I." See the trouble?
The English section of the ACT contains 75 questions, which you must answer in 45 minutes. More than 50 percent of the English section tests standard English conventions, such as sentence structure and formation, punctuation and usage. Pronouns are a part of these conventions.
You all know what pronouns are, so we will not discuss that here. You also know how to use them: a substitute for a noun. Things get complicated when pronouns take on different guises, depending on the roles in plays in the sentence. Some pronouns are so well disguised that you may not be able to tell one from another. The usual suspects are: that and which; it's and its; who's and whose; who and whom; everybody and nobody; and their, they're, and theirs.

The 'Which' Trials

Which vs That Trials
Image from Pixabay
  • Nobody likes a dog that bites.
  • Nobody likes a dog which bites.

Which sentence sounds right to you? If both did, you got 'which-ed'! The first sentence with 'that' is the correct usage. A lot of students (and adults) have problems with that-versus-which. Here are two rules that can help you figure out whether a clause should start with that or which.

  1. If you can drop the clause and not lose the point of the sentence, use which. If you can't, use that.
  2. A which clause goes inside commas. A that clause doesn't.

Let's look at these sentences:​
  • Buster's bulldog, which had one white ear, won best in show.
  • The dog that won best in show was Buster's bulldog.

The point of each sentence is that Buster's bulldog won. What happens when we remove the that or which clause? In the first example, the which clause is disposable. We can just say: Buster's bulldog won best in show. In the second example, however, the that clause (that won best in show) is essential. Without it the sentence would read: The dog was Buster's bulldog, which is a different meaning that the dog that won best in show was Buster's bulldog.

Who vs. Whom

When do you 'who' and when do you use 'whom'? Keep it simple! The most important thing to know is that who does something (it's a subject, like she), and whom has something done to it (it's an object, like her). Sometimes it can get tricky. Let's see the following examples:

  • Amanda invited only girls [who or whom] she thought used math for fashion design.

Is it 'who' or 'whom'? If you strip off all the words between the subject and verb, you end up with who ... used math for fashion. 'Who' did something (used math for fashion), so it's the subject. 'Whom' does not work.
​
  • Tom wouldn't tell Miss Marple [who or whom] he invited to his bowling game.

First strip the sentence down to the basic clause, [who or whom] he invited. You can see that whom is the object--he did something to (invited) whom--even though whom comes ahed of both the subject and the verb.

More than Meets the I

Many smart people hesitate about I vs me, he vs him, she vs her, and they vs them. How do we use them correctly? It all depends on the context. Let's look at the following examples:

  • Mary loves pasta more than I. Here it means that she likes pasta more than I do.
  • Mary loves pasta more than me. Here it means that she loves pasta more than she loves me!

So the usage of I vs me depends on the context, i.e., what you are trying to communicate.

The Many Selves

Students (and adults) often confuse the usage of 'I' and 'myself' and the rest of the 'self' crew (yourself, himself, herself, itself, ourselves, yourselves, themselves). The key point about the 'self' crew is that they should not take the place of ordinary pronouns I and me, she or her, and so on. They are used only for two purposes:
​
  • To emphasize. I made the cake myself. The detective himself was the murderer. 
  • To refer to the subject. She hates herself. And you call yourself a mechanic! They consider themselves lucky to be alive. The problem surprisingly solved itself.
There are some other pesky pronouns, but that topic is for another blog.
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How to Use the Unloved Semicolon and the Formidable Colon

11/22/2017

 
What to use? Semicolon or Colon?
Grammar.net [Infographic provided by Grammar.net]
The semicolon is one of the most useful but least used punctuation marks.

The Semicolon

Many people avoid the semicolon. Some even seem to dislike it, but it does not have to be that way. The source of avoidance or dislike is the lack of understanding of the proper role of the semicolon. If a comma is a yellow light and a period is a red light, the semicolon is a flashing red--one of the lights you drive through a brief pause. 

Here's when to use it.
1. Use a semicolon to separate clauses when there's no and in between. 
  • Sam's hat flew off his head; it sailed into the distance.
2. Use semicolons to separate items in a series when there's already a comma in one or more of the items.
  • Amanda's favorite things were her robe, a pink sweater from Grandma; her slippers; her overstuffed chair, which had once been her grandfather's; mystery stories, especially by Agatha Christie and Sherlock Holmes.

The Colon

Think of the colon as punctuation's master of ceremonies. Use it to present something: a statement, a series, a quotation, or instructions. But remember that a colon is an abrupt stop, almost like a period. Use one only if you want your sentence to brake completely. Here is how to do it.
1. Use a colon instead of a comma, if you wish, to introduce a quotation.
  • I said to her: "Jane, please pick up a bottle of wine on your way over. But don't spend too much time looking. Just pick a Merlot." 

Many people prefer to introduce a longer quotation with a colon instead of a comma.
2. Use a colon to introduce a list, if what comes before the colon could be a small sentence in itself (it has both a subject and a verb).
  • John brought three wines: a Bordeaux, a Merlot, and a Chardonnay.

Just don't use the colon to separate a verb from the rest of the sentence. In John's shopping cart were: a Bordeaux, a Merlot, and a Chardonnay. If you don't need a colon, why use one? In John's shopping cart were a Bordeaux, a Merlot, and a Chardonnay.
And that's it folks. Wasn't that easy?
Reference: Woe is I, by Patricia T. O'Connor
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13 Comma Rules You Need to Know to Soar on Tests

11/2/2017

 
Comma rules
Grandpa and commas
The comma is a small mark, but it is perhaps the most important punctuation in grammar. Despite that, comma confusion is one of the most common grammatical problems that students face. This blog attempts to help students with proper comma usage.

Short Summary (TL;DR)

Comma Usage:
  1. The pause
  2. Separate parts of speech
  3. Never separate subject from its verb
  4. After Introductory phrase, clause, word
  5. Separate clauses when using FANBOYS
  6. Relative clauses
  7. Non-relative clauses
  8. "that" clauses
  9. 'Keep' the essential and ​'cut out' the non-essentials
  10. Geography, Dates, Addresses and Titles
  11. Series or list
  12. Shift between the main discourse and a quotation​
  13. Contrasts​

1. The Pause

​Commas, commas, commas. They often are a source of confusion. How do you use without getting lost in grammatical jargon? Thanks to Patricia T. O’Conner's book on grammar, Woe is I: The Grammarphobe’s Guide to Better English in Plain English, commas can easily be understood. We let her tell you about them in her own words:

"When you talk, your voice, with its pauses, stresses, rises and falls, shows how you intend your words to fit together. When you write, punctuation marks are the road signs (stop, go, yield, slow, detour) that guide the reader, and you wouldn’t be understood without them.
"If you don’t believe me, try making sense out of this pile of words:
Who do you think I saw the other day the Dalai Lama said my Aunt Minnie.

"There are at least two possibilities:

"Who do you think I saw the other day?" the Dalai Lama said. "My Aunt Minnie."
"Who do you think I saw the other day? The Dalai Lama!" said my Aunt Minnie."

​
"Punctuation isn’t some subtle, old-fashioned concept that’s hard to manage and probably won’t make much of a difference one way or another. It’s not subtle, it’s not difficult and it can make all the difference in the world.

2. Separate the Parts of Speech

If you get commas right, you will get most of your punctuation right. How do we use them?
Long and short division
Use a comma to separate big chunks (clauses) of a sentence with and between them. 
  • Samantha hadn’t left the city in months, and by Sunday she was climbing the walls. 

If there’s no 'and' in between, use a semi-colon instead: 
  • Samantha hadn’t left the city in months; by Sunday she was climbing the walls.

Use commas to separate a series of things or actions. 
  • She packed a toothbrush, a blow-dryer, her swimsuit and her teddy bear.
  • ​She finished packing, paid some bills, ate a few Oreos and watered the plants.

In a series, you can leave out the comma before "and". It’s just a matter of taste. 'And' can also be thought of as a separator, a break, so a comma often is unnecessary.

3. Comma with Subjects and their Verbs

With few exceptions, a comma should not separate a subject from its verb.

Incorrect: My friend Amanda, is a wonderful dancer.

Writers are often tempted to insert a comma between a subject and verb this way because speakers sometimes pause at that point in a sentence. But in writing, the comma only makes the sentence seem stilted.

Correct: My friend Amanda is a wonderful singer.

Be especially careful with long or complex subjects:
​
Incorrect: The things that cause me joy, may also cause me pain.
Correct: The things that cause me joy may also cause me pain.
Incorrect: Navigating through snow, sleet, wind, and darkness, is a miserable way to travel.
Correct: Navigating through snow, sleet, wind, and darkness is a miserable way to travel.

4. Comma After Introductions

Introductory Clauses
Introductory clauses are dependent clauses that provide background information or "set the stage" for the main part of the sentence, the independent clause. For example:
  • If they want to win, athletes must exercise and practice every day.

​Introductory phrases
Introductory phrases also set the stage for the main action of the sentence, but they are not complete clauses. Phrases don't have both a subject and a verb that are separate from the subject and verb in the main clause of the sentence. Common introductory phrases include prepositional phrases, appositive phrases, participial phrases, infinitive phrases, and absolute phrases.
  • To stay in shape for competition, athletes must exercise every day.  (Introductory infinitive phrase, main clause)
  • Barking insistently, Smokey got us to throw his ball for him. (Introductory participial phrase, main clause)
  • A popular and well respected mayor, Bailey was the clear favorite in the campaign for governor. (introductory appositive phrase, main clause)
  • The wind blowing violently, the townspeople began to seek shelter. (introductory absolute phrase, main clause)
  • After the adjustment for inflation, real wages have decreased while corporate profits have grown. (introductory prepositional phrases, main clause)

​Introductory words (SHFM)
Introductory words like however, still, furthermore, and meanwhile create continuity from one sentence to the next.
  • The coaches reviewed the game strategy. Meanwhile, the athletes trained on the Nautilus equipment.
  • Most of the evidence seemed convincing. Still, the credibility of some witnesses was in question.

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This is What You Need to Know to Deliver Drugs to the Colon on the ACT

7/24/2017

 
human system
Photo by Samuel Zeller on Unsplash
Traditionally, oral drugs in pill or capsule form have been designed to release the dose of medicine in the upper gastrointestinal tract, where drugs are more readily dissolved and absorbed. New research has targeted the colon as an ideal environment for drug absorption to treat certain illnesses. To reach the colon, the drug must first pass through the stomach and small intestine. Table 1 details several drug-delivery systems. 
act drug colon table 1
The following experiments test two of the drug-delivery systems: 

Experiment 1
Bacteria-dependent delivery. This experiment measured the average time it took a coated tablet to travel from the stomach (gastric emptying) through the small intestine (small intestine transit) to arrive in the colon. Twelve healthy men aged 23 to 25 years old and weighing between 55 and 70 kilograms (kg) who had fasted overnight were divided into 3 groups. They each swallowed 1 tablet, which contained a tracer (A or B) and 1 of 2 natural coatings (1 or 2). The location of the tracer was measured every half-hour for 12 hours. The average times are recorded in Table 2. 
act drug colon table 2

Experiment 2
Time-dependent delivery. The methods were the same as those used in Experiment 1, except that the tablets all contained the same tracer and 1 of 2 outer coatings (A or B) and one of two inner coatings (1 or 2). The average times are recorded in Table 3. 
act science colon drug table 3

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How to Control Salmonella Growth on the ACT

7/21/2017

 
Salmonellosis
Several scientists considered some different environmental factors and their influence on the growth of certain bacteria. The following experiments used Salmonella bacteria to measure the effect of pH levels, nutrients, and temperature on the number of bacteria produced within a given time period.
Experiment 1

​A known quantity of 
Salmonella bacteria was placed in 
each of 3 Petri dishes with the same nutrient concentration at the same temperature. The pH level of each nutrient con- centration in each dish was varied according to Table 1. On the pH scale, 7 represents neutral, values less than 7 indicate an acid, and values greater than 7 indicate a base. The lids of the Petri dishes were replaced after the bacteria were added and the dishes were left alone. After 6 hours, the percent growth of Salmonella bacteria was recorded (Table 1). ​
salmon table 1
Experiment 2

A known quantity of Salmonella bacteria was placed in
each of 3 Petri dishes with different nutrient concentrations in the form of organic compounds. The temperature and pH level (neutral 7) were held constant in each sample. The lids of the Petri dishes were replaced after the bacteria were added and the dishes were left alone. After 6 hours, the percent growth of Salmonella bacteria was recorded (Table 2). 

​
salmon table 2
Experiment 3

A known quantity of Salmonella bacteria was placed in
each of 3 Petri dishes at different temperatures. The pH level and nutrient concentrations were held constant. The lids of the Petri dishes were replaced after the bacteria were added and the dishes were left alone. After 6 hours, the percent growth of Salmonella bacteria was recorded (Table 3). 
salmon table 3

Questions:

1. According to Table 1, what might best contribute to the growth of Salmonella bacteria?

A. A pH level above 9
B. A pH level below 5
C. A pH level near 7
D. A pH level near 5 

​
2. According to the results of the three experiments, which combination of the three factors studied would be expected to produce the highest percent growth?

F. pH level of 5, organic compound in Dish 2, temperature of 40◦C
G. pH level of 7, organic compound in Dish 2, temper- ature of 10◦C
H. 
pH level of 5, organic compound in Dish 1, temper- ature of 40◦C
J. pH level of 9, organic compound in Dish 1, temper- ature of 90◦C 

​
3. Which of the following conclusions is strengthened by the results of Experiment 1?

A. Salmonella bacteria reproduce most efficiently in an acidic environment.
B. Salmonella bacteria reproduce most efficiently in a neutral environment.
C. Salmonella bacteria cannot reproduce in a basic environment.
D. Salmonella bacteria cannot reproduce in an acidic environment. 

​
4. Bacteria will generally reproduce until all of the nutrients available have been depleted. How could the experiment be altered to maximize the length of time that bacteria will reproduce?

F. Change the observation time from 6 hours to 12 hours.
G. Regularly re-supply each group of bacteria with unlimited nutrients.
H. Increase the rate of growth by decreasing the pH levels.
J. Do not test the effect of different nutrient combinations on growth.

5. Which of the following was the independent variable in Experiment 3?

A. pH level
B. temperature
C. organic compound
D. percent growth 

​
6. The experiments recorded the percent growth that occurred over a 6-hour period. Bacteria often repro- duce at a rate that drastically varies from one stage to the next. The best way to study the different stages of growth would be to record the percent growth: 

F. after 2 hours only.
G. after 4 hours, then again after 6 hours.
H. after 8 hours only.
J. every 15 minutes for 3 hours. 

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This is What Happens to Your Dopamine Level on the ACT

7/12/2017

 
Dopamine levels on the ACT
Image from Pixabay
Dopamines serve as enhancers or catalysts (a substance that initiates or increases the rate of impulses during a chemical reaction, but is not depleted during the process) to certain reactions involved in the activity of human thought. The dopamine intropin is involved in the stimulation of the neurotransmitters in the brain when thought is initiated. A student investigated the effects of dopamine activity on a specific neurotransmitter. 
Experiment 1

To each of 10 test tubes, 7 milliliters (mL) of a peptide (a neurotransmitter) solution was added. Two mL of an intropin solution was added to each of Tubes 1–9. Tube 10 received 2 mL of water without intropin. The tubes were then stirred at a constant rate in water baths at various temperatures and incubated (heated) from 0 to 15 minutes (min). At the end of the incubation period, 0.3 mL of NaCl solution was added to each tube. The NaCl stopped the reaction between the intropin and the peptide. The precipitates, solids formed in a solution during a chemical reaction, which in this case were caused by the reaction of NaCl and the pep- tide, were removed from the tubes and dried. The masses of the precipitates, in milligrams (mg), were measured to determine the relative amount of enhancer that remained in the tube. The results are shown in Table 1. 
table 1 dopamine
Experiment 2

Peptide solution (8 mL) was added to an additional 8 test tubes to which 2 mL of intropin solution was then added. The tubes were incubated at 10 degrees Celsius and stirred at a constant rate for 15 min. The effect of acidity on the neurotransmitter was observed by varying the acidity levels (using the pH scale). The relative amount of neurotransmitter present in each tube was determined in the same manner as Experiment 1, by adding NaCl solution to each test tube. The results are in shown in Table 2. 
table2_dopamine

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Solving this Complex Number Problem on the ACT will Make you Smarter

6/29/2017

 
Complex numbers on the ACT
In the complex plane, the horizontal axis is called the real axis and the vertical axis is called the imaginary axis. The complex number a + bi graphed in the complex plane is comparable to the point (a, b) graphed in the standard (x, y) coordinate plane. The modulus of the complex number a + bi is given by:
\[\sqrt{a^2 + b^2}\]

Question:

Which of the complex numbers z1, z2, z3, z4 and z5 below has the greatest modulus?
Picture

Answer:

Okay, so what is this question really asking?

All it is asking is for you to find the largest value of the square root of the sum of the squares of our coordinate p
oints, or find:
\[\sqrt{x^2 + y^2}\]
The challenge is that we are not given the real x and y values of the coordinate points. So we have to estimate the coordinate points of our z points. 

Because we are working with squares, negatives are not a factor, so we can eliminate the smaller numbers as we are just taking a number, positive or negative and taking the square of it. Let us estimate our coordinates:
​

z1 = (-4, 5)
z2 = (-2, 1)
z3 = (-2, 3)
z4 = (2, -2)
z5 = (4, 2)

We are looking for whichever point has the largest combination of its coordinate points. At a glance, the two points with the largest coordinates are z1 and z5. Let's find the modulus of z5, and smaller of the two.
\[\sqrt{4^2 + (-2)^2}\]
\[\sqrt{16 + 4}\]
\[\sqrt{20}\]
\[4.5\]
And the modulus of z1:
\[\sqrt{(-4)^2 + 5^2}\]
\[\sqrt{16 + 25}\]
\[\sqrt{41}\]
\[6.4\]
We can see that the modulus of z1, 6.4,  is higher than that of z5.

Final answer: F, z1.
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Can you Solve this One of the Hardest Problems on the ACT?

6/23/2017

 
Picture

Question:

Consider the functions f(x) = sqrt(x) and g(x) = 7x + b. In the standard (x,y) coordinate plane, y = f(g(x)) passes through (4,6). What is the value of b?

A. 8
B. -8
C. -25
D. -26
E. 4 - 7. sqrt(6)

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How to Solve this Greatest Common Factor Challenge on the ACT

6/15/2017

 
greatest common factor

Two whole numbers have a greatest common factor of 8 and a least common multiple of 48. Which of the following pairs of whole numbers will satisfy the given conditions?

F. 4 and 9
G. 5 and 10
H. 10 and 16
J. 14 and 20
K. 16 and 24 

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How to Find the Best Nonstick Cookware on the ACT Science

6/13/2017

 
nonstick cookware

A group of students conducted several experiments using a variety of nonstick cookware, a spring scale, and several different weighted objects. Their goal was to determine which brand of cookware products had the best nonstick surface by measuring the coefficient of static friction, which is a measure of how resistant a stationary object is to movement.

Experiment 1
A student connected the spring scale to a weighted object that was placed inside a piece of nonstick cookware as shown in Figure 1.

The students planned to calculate the coefficient of static friction by determining the force required to disturb an object from rest. During the experiment, one student anchored the nonstick cookware be holding tightly to the handle while the other student attached a weighted, smooth steel object to the spring scale. The student pulled on the spring until the object began to move. A third student recorded the force in newtons, N, indicated on the spring scale at the moment the object began to move across the nonstick surface.

This procedure was repeated for 3 different brands of cookware; each brand of cookware was tested with various weighted objects. The coefficient of static friction was calculated by dividing the average force required to move the object by its weight (mass × g, the gravitational constant). The results are shown in Table 1.
act science table 1
Experiment 2
The students performed an experiment similar to Experiment 1, except three different brands of cooking spray were applied to the same cookware surface before the weights were put in place. The results are shown in Table 2.
act science table 2

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How to Solve this Problem of the Fishermen on the ACT

6/6/2017

 
fishermen and math

Problem

A total of f men went on a fishing trip. Each of the r boats that were used to carry the fishermen could accommodate a maximum number of m passengers. If one boat had 5 open spots and the remaining boats were filled to capacity, which of the following expresses the relationship among f , r, and m?
​

F. rm+5=f
G. rm−5=f
H. r+m+5=f

J. rf = m + 5
​
K. rf = m − 5 



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How to Solve Class Scheduling Problems on the ACT

4/11/2017

 
Randall is scheduling his classes for next term. He has a choice of 3 different science classes, 4 different math classes, and 5 different humanities classes. How many different class schedules can Randall create if he must take 1 science class, 1 math class, and 1 humanities class?
​

F. 14
G. 23
H. 30
J. 45
K.
60 


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How to Show your Friends’ Favorite Ice Cream Flavors on the ACT

1/12/2017

 

Question:

John wants to draw a circle graph showing his friends’ favorite ice cream flavors. When he polled his friends asking each their favorite flavor of ice cream, 35% of his friends said chocolate, 20% of his friends said vanilla, 15% of his friends said strawberry, 25% of his friends said mint chocolate chip, and 5% of his friends said flavors other than those previously listed. What will be the degree measure of the vanilla sector of the circle graph?


A. 126◦
B. 108◦
C. 90◦
D. 72◦
​
E. 36
◦ 




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How to Calculate the Amount of Flour for Baking on the ACT

1/5/2017

 

Question

When baking cookies, the quantity of flour needed is a constant proportion of the number of cookies being made. If 24 cookies require 2 cups of flour, how many cups of flour will 60 cookies require? 


F. 2
G. 2  1/4 

H. 3
J. 4  1/2

K. 5




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In What Year did Teenagers Buy the Most CDs and Video Games?

1/3/2017

 

Question

It is estimated that, from the beginning of 1995 to the end of 1999, the average number of CDs bought by teenagers increased from 5 per year to 9 per year. During the same time period, the average number of videogames purchased by teen- agers increased from 2 per year to 10 per year. Assuming that in each case the consumption rates are the same, in what year did teenagers buy the same average number of CDs and videogames?

A. 1995
B. 1996
C. 1997
D. 1998
E.
1999 


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How many People do not have a White House on the ACT?

12/27/2016

 

Question

In a town called Hortonville, exactly 648 of the 2,160 residents have a white house. What percentage of the Hortonville residents does NOT have a white house?


F. 30%
G. 50%
H. 70%
J. 80%
​
K.
90% 


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How to Avoid Yellow Fever on the ACT

11/30/2016

 

Direction:

In the passage that follow, some words and phrases are underlined and numbered. In the answer column, you will find alternatives for the words and phrases that are underlined. Choose the alternative that you think is best, and fill in the corresponding bubble on your answer sheet. If you think that the original version is best, choose “NO CHANGE,” which will always be either answer choice A or F. 

Passage and Questions:

Walter Reed’s Medical Breakthrough 

Just over 100 years ago, one of the most important medical discoveries, in modern times [1] relieved the suffering [1] and saved the lives of untold thousands. This major breakthrough was the identification of the cause and spread of the disease yellow fever.

​For several centuries, yellow 
fever was a scourge upon societies [2] in various parts of the world, striking towns and killing thousands of people. Thanks to [3] the efforts of Major Walter Reed and many courageous volunteers, the mechanisms for contracting and spreading yellow fever were uncovered. 

During Reed’s lifetime, it was a common acceptance [4] that yellow fever was spread by contact with infected items; such as [5] the clothing or blankets of a person with yellow5fever. Some doctors, however, questioned this notion, as the spread of yellow fever was not consistent 
with the spread of other communicable diseases [6].


Doubts about the accepted theory’s [7] of the fever’s spread prompted the U.S. Army to assign Reed and several doctors to the problem. They studied yellow fever in Cuba, where they were [8] infecting soldiers fighting in the Spanish 8 American War at a discouraging [9] rate. Acting on a hunch, several doctors volunteered to be bitten by mosquitoes; the volunteers developed yellow fever. This was enough information to spur General Reed to conduct more comprehensive experiments, so helping his cause [10].


[6.] 

Which of the following sentences, if inserted here, would be the best example of how yellow fever seemed to be spread differently than other communicable diseases? 

F.  For example, people had no choice but to wear clothing and use blankets, so the fever could not have spread that way. 
G. For example, sometimes one person would get sick in a household, while nobody else in that household would get sick. 

H. For example, yellow fever caused a great deal of pain in its victims. 

J. For example, some doctors were willing to go against what the rest of the medical establishment was saying.



[7.]

A. 
NO CHANGE 
B. theorize 

C. theories’ 
D. theories


[8].
F. 
NO CHANGE 
G. the disease was 
H. the doctors were 

J. the Army was


[9]. The writer wants to emphasize how quickly yellow fever was infecting the troops in the Spanish American War. Which choice does that best?

A. NO CHANGE 

B. a great
C. an alarming 
D. a normal 


[10].

F. 
NO CHANGE
G. experiments; which helped his cause. 
H. experiments (which helped his cause). 

J. experiments. 

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How to calculate Cosines, Sines and Tangents on the ACT

11/29/2016

 

Question:

If cos x = 5/7 and tan x = 4/5, what is sin x?

A. 4/7
B. 7/9
​C. 5/4
​D. 9/7
E. 7/5



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How to Calculate Simple Interest on the ACT

11/28/2016

 

Question:

A formula for calculating simple interest is I = Pr, were I is the interest earned in dollars, P is the principal or original investment, and r is the fixed rate of interest. If the amount of interest earned is $2.25 and the interest rate is 3%, what is P?

F. $6.75
G. $7.50
H. $13.30
J. $67.50
K.
$75.00 


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